Related papers: On Essential and Topologically Essential Submodule…

In the first part of the paper, we use states on $C^*$-algebras in order to establish some equivalent statements to equality in the triangle inequality, as well as to the parallelogram identity for elements of a pre-Hilbert $C^*$-module. We…

We introduce a similarity relation between submodules of a module $M$ over a ring $R$, extending the classical notion of similarity for right ideals. Focusing on (faithfully) projective modules, we establish a sharp lower bound for the…

In Rev. Math. Phys. 4 (1997) 785 we study Hilbert-C* systems {F,G} where the fixed point algebra A has nontrivial center Z and where A'\cap F=Z is satisfied. The corresponding category of all canonical endomorphisms of A contains…

Let $A$ be a unital $C^*$-algebra containing a closed two-sided ideal $J$ and an operator system $X$. We enlarge $X$ to an operator system $\mathcal{S}(X,J)$ in $\mathbb{M}_2(A)$, and show that in order for $\mathcal{S}(X,J)$ to be…

Let $S = (S_1, \ldots, S_d)$ denote the compression of the $d$-shift to the complement of a homogeneous ideal $I$ of $\mathbb{C}[z_1, \ldots, z_d]$. Arveson conjectured that $S$ is essentially normal. In this paper, we establish new results…

We introduce the notion of the separated pair of closed submodules in the setting of Hilbert $C^*$-modules. We demonstrate that even in the case of Hilbert spaces this concept has several nice characterizations enriching the theory of…

Following up on previous work, we prove a number of results for C*-algebras with the weak ideal property or topological dimension zero, and some results for C*-algebras with related properties. Some of the more important results include:…

In this paper we survey our recent work on C*-correspondences and their associated operator algebras; in particular, on adding tails, the Shift Equivalence Problem and Hilbert bimodules.

Given two C*-algebras A and B, abstract A-B bimodules that can be isometrically represented as operator bimodules are characterised in terms of their norm. Various properties of such bimodules are given. Their theory is very similar to…

Let $A$ be a simple C*-algebra of stable rank one and let $p$ and $q$ be two $\sigma$-compact open projections. It is proved that there is a continuous path of unitaries in ${\tilde A}$ which connects open sub-projections of $p$ which is…

We introduce a classification of locally compact Hausdorff topological spaces with respect to the behavior of $\sigma$-compact subsets, and relying on this classification we study properties of corresponding $C^*$-algebras in terms of frame…

We give a notion of equivalence for Fell bundles over groups, not necessarily saturated nor separable, and show that equivalent Fell bundles have Morita-Rieffel equivalent cross-sectional $C^*$-algebras. Our notion is originated in the…

It is shown that if A is a stably finite C*-algebra and E is a countably generated Hilbert A-module, then E gives rise to a compact element of the Cuntz semigroup if and only if E is algebraically finitely generated and projective. It…

Let $A$ be a $C^*$-algebra. Let $E$ and $F$ be Hilbert $A$-modules with $E$ being full. Suppose that $\theta : E\to F$ is a linear map preserving orthogonality, i.e., $<\theta(x), \theta(y) > = 0$ whenever $<x, y > = 0$. We show in this…

We consider two inclusions of $C^*$-algebras whose small $C^*$-algebras have approximate units of the large $C^*$-algebras and their two spaces of all bounded bimodule linear maps. We suppose that the two inclusions of $C^*$-algebras are…

We investigate the notion of conditionally positive definite in the context of Hilbert $C^*$-modules and present a characterization of the conditionally positive definiteness in terms of the usual positive definiteness. We give a Kolmogorov…

We show that the gluing construction for Hilbert modules introduced by Raeburn in his computation of the Picard group of a continuous-trace C*-algebra (Trans. Amer. Math. Soc., 1981) can be applied to arbitrary C*-algebras, via an algebraic…

The overview contains 450 references of books, chapters of monographs, papers, preprints and Ph.~D.~thesises which are concerned with the theory and/or various applications of Hilbert C*-modules. To show a way through this amount of…

We provided an analogue Banach-Alaoglu theorem for Hilbert $H^*$-module. We construct a $\Lambda$-weak$^*$ topology on a Hilbert $H^*$-module over a proper $H^*$-algebra $\Lambda$, such that the unit ball is compact with respect to…

We show that, when $A$ is a separable C*-algebra, every countably generated Hilbert $A$-module is projective (with bounded module maps as morphisms). We also study the approximate extensions of bounded module maps. In the case that $A$ is a…